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SEISMIC FEATURE EXTRACTION USING STEINER TREE METHODS
"... Identifying “interesting” features, such as faults, unconformities, and other events in subsurface images is a challenging task in seismic data processing. Existing stateoftheart methods usually involve manual intervention in the form of a visual inspection by an expert, but this is timeconsumin ..."
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Identifying “interesting” features, such as faults, unconformities, and other events in subsurface images is a challenging task in seismic data processing. Existing stateoftheart methods usually involve manual intervention in the form of a visual inspection by an expert, but this is timeconsuming, expensive, and errorprone. In this paper, we propose an efficient, automatic approach for seismic feature extraction. The core idea of our approach involves interpreting a given 2D seismic image as a function defined over the vertices of a specially chosen underlying graph. This enables us to formulate the feature extraction task as an instance of the PrizeCollecting Steiner Tree problem encountered in combinatorial optimization. We develop an efficient algorithm to solve this problem, and demonstrate the utility of our method on a number of synthetic and real examples.
Fast Algorithms for Structured Sparsity (ICALP 2015 Invited Tutorial)
"... Sparsity has become an important tool in many mathematical sciences such as statistics, machine learning, and signal processing. While sparsity is a good model for data in many applications, data often has additional structure that goes beyond the notion of “standard ” sparsity. In many cases, we ca ..."
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Sparsity has become an important tool in many mathematical sciences such as statistics, machine learning, and signal processing. While sparsity is a good model for data in many applications, data often has additional structure that goes beyond the notion of “standard ” sparsity. In many cases, we can represent this additional information in a structured sparsity model. Recent research has shown that structured sparsity can improve the sample complexity in several applications such as compressive sensing and sparse linear regression. However, these improvements come at a computational cost, as the data needs to be “fitted ” so it satisfies the constraints specified by the sparsity model. In this survey, we introduce the concept of structured sparsity, explain the relevant algorithmic challenges, and briefly describe the best known algorithms for two sparsity models. On the way, we demonstrate that structured sparsity models are inherently combinatorial structures, and employing structured sparsity often leads to interesting algorithmic problems with strong connections to combinatorial optimization and discrete algorithms. We also state several algorithmic open problems related to structured sparsity. 1